The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  X  1  1  1 X^2  1  1  X  1  0  1  1  1 X^2+X  1  X  0  1  1  1  1  1 X^2+X X^2  1  X  1  1 X^2  1  X  0  X  1
 0  1  1  0 X^2+X+1  1  X X+1  1 X^2+X  1 X^2+1 X^2+X+1  0  1 X^2+1  X  1  1  1 X^2+X X^2+X+1 X^2+X  1 X^2+X  1  1  0  1 X+1  X  0  1  1 X^2+1 X^2  X  1  1  0  1  1  1  0
 0  0  X  0 X^2+X  0  0  X X^2  0 X^2  X  0 X^2+X X^2+X X^2  X X^2+X  0 X^2+X X^2+X X^2  0 X^2+X  0  X  X X^2+X X^2  0  X  X  X  0  X X^2 X^2+X  X X^2 X^2+X X^2+X  X X^2+X  X
 0  0  0  X  0  0  X  X X^2+X X^2  X  X X^2+X  X  0 X^2  0  X  X X^2+X X^2+X  X X^2 X^2+X  X  0 X^2+X X^2+X  X X^2 X^2 X^2+X  X  X  0  X  0  X X^2+X  X X^2+X  0  0  X
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2  0  0  0 X^2 X^2  0  0
 0  0  0  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0
 0  0  0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2

generates a code of length 44 over Z2[X]/(X^3) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+64x^36+108x^37+162x^38+432x^39+359x^40+846x^41+590x^42+1172x^43+730x^44+1240x^45+631x^46+832x^47+321x^48+328x^49+118x^50+116x^51+54x^52+36x^53+30x^54+8x^55+7x^56+2x^57+4x^58+1x^62

The gray image is a linear code over GF(2) with n=176, k=13 and d=72.
This code was found by Heurico 1.16 in 2.36 seconds.